During many cell processes, the shape of the cell undergoes various transformations. The variety of red blood cell shapes is well documented. The immediate objectives are to understand the dynamical basis of some of the red cell shape changes - osmotic swelling, crenation and cupping. In this way the most important components (elasticity, viscosity, bending intrinsic curvature) that control the characteristics and time scales can be identified. A continuum approach will be used to model these cell transformations. The interior of the red cell (hemoglobin) can be viewed as a viscous incompressible fluid, while the membrane is modelled by a two dimensional continuum of viscoelastic material (fluid or solid). The dynamic response of such an encapsulated droplet to various stimuli will allow the evolution of the shape of the drop/cell with time to be studied. Osmotic swelling of the bioconcave disk to sphere observed in hypotonic solution will be modelled by mass transport of fluid across the membrane. Crenation and cupping of red cells are thought to evolve from preferential placement of molecules into the outer or inner half of the membrane bilayer. It is unclear whether the bilayer is connected or unconnected. A comprehensive study of the dynamics of bilayers as two monolayers which cannot/can slide over one another will be undertaken. In this way changes in either half of the bilayer can be examined and the deformation that ensues can be determined. Protuberances often occur at local sites on the surface. A study of the response of droplets to local changes in the interior or surface (local osmosis, local binding of material or change in membrane chemical composition) will be initiated. A continuum approach requires the formulation of equations of motion, conservation of mass and bending moments and balance of stresses arising from viscous, elastic and surface tension forces. The resulting system is a moving boundary value problem, so that the equations describing the drop surface and the motion of the fluids must be solved simultaneously. The proposed research will provide a better understanding of the dynamical basis of shape tranaformations. This is important for an understanding of the membrane structure of the red cell and its ability to deform into restricted regions of the microcirculation.